Quantum digital-to-analog conversion algorithm using decoherence

Saitoh, Akira

doi:10.1007/s11128-015-1033-x

Cited by 2 publications

(1 citation statement)

References 59 publications

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“…Once computed, a conversion back to quantum-amplitude representation is to be used, enabling the rest of the quantum algorithm to proceed. For this 'digital-to-analog' conversion, quantum algorithms were recently studied and published by SaiToh [26]. For the representation in the computational basis, a fixed-point approach is typically employed to represent real or complex numbers in quantum algorithms.…”

Section: Representing Nonlinear Terms In Computational Basismentioning

confidence: 99%

Quantum Algorithms for Nonlinear Equations in Fluid Mechanics

Steijl¹

2022

Quantum Computing and Communications

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In recent years, significant progress has been made in the development of quantum algorithms for linear ordinary differential equations as well as linear partial differential equations. There has not been similar progress in the development of quantum algorithms for nonlinear differential equations. In the present work, the focus is on nonlinear partial differential equations arising as governing equations in fluid mechanics. First, the key challenges related to nonlinear equations in the context of quantum computing are discussed. Then, as the main contribution of this work, quantum circuits are presented that represent the nonlinear convection terms in the Navier–Stokes equations. The quantum algorithms introduced use encoding in the computational basis, and employ arithmetic based on the Quantum Fourier Transform. Furthermore, a floating-point type data representation is used instead of the fixed-point representation typically employed in quantum algorithms. A complexity analysis shows that even with the limited number of qubits available on current and near-term quantum computers (<100), nonlinear product terms can be computed with good accuracy. The importance of including sub-normal numbers in the floating-point quantum arithmetic is demonstrated for a representative example problem. Further development steps required to embed the introduced algorithms into larger-scale algorithms are discussed.

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Section: Representing Nonlinear Terms In Computational Basismentioning

confidence: 99%

Quantum Algorithms for Nonlinear Equations in Fluid Mechanics

Steijl¹

2022

Quantum Computing and Communications

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Quantum Circuit Implementation of Multi-Dimensional Non-Linear Lattice Models

Steijl

2022

Applied Sciences

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The application of Quantum Computing (QC) to fluid dynamics simulation has developed into a dynamic research topic in recent years. With many flow problems of scientific and engineering interest requiring large computational resources, the potential of QC to speed-up simulations and facilitate more detailed modeling forms the main motivation for this growing research interest. Despite notable progress, many important challenges to creating quantum algorithms for fluid modeling remain. The key challenge of non-linearity of the governing equations in fluid modeling is investigated here in the context of lattice-based modeling of fluids. Quantum circuits for the D1Q3 (one-dimensional, three discrete velocities) Lattice Boltzmann model are detailed along with design trade-offs involving circuit width and depth. Then, the design is extended to a one-dimensional lattice model for the non-linear Burgers equation. To facilitate the evaluation of non-linear terms, the presented quantum circuits employ quantum computational basis encoding. The second part of this work introduces a novel, modular quantum-circuit implementation for non-linear terms in multi-dimensional lattice models. In particular, the evaluation of kinetic energy in two-dimensional models is detailed as the first step toward quantum circuits for the collision term of two- and three-dimensional Lattice Boltzmann methods. The quantum circuit analysis shows that with O(100) fault-tolerant qubits, meaningful proof-of-concept experiments could be performed in the near future.

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Quantum digital-to-analog conversion algorithm using decoherence

Cited by 2 publications

References 59 publications

Quantum Algorithms for Nonlinear Equations in Fluid Mechanics

Quantum Algorithms for Nonlinear Equations in Fluid Mechanics

Quantum Circuit Implementation of Multi-Dimensional Non-Linear Lattice Models

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